Use the acceleration output of the Euler-Lagrange equations to construct a state-derivative function for a system...

 

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Use the acceleration output of the Euler-Lagrange equations to construct a state-derivative function for a system with specified inertia, inertia-derivative, and force functions. In addition to standard Matlab functions, your code may assume that you have access to the following function(s) you created in previous assignments (along with the functions that they themselves call): ■ EulerLagrange_acceleration Remember that for these functions, the grading script will use the instructor's copy of the functions. function [state_velocity,.... configuration,... velocity,... acceleration] = Euler Lagrange_trajectory (time, state,M_function, dM_function, F_function) % Follow a trajectory whose acceleration is determined by an inertia matrix % and forcing function % % Inputs: % % % % % % % % % % % % % % % time: A scalar value describing the time at which the system dynamics are evaluated % 0/ state: A (2n)x1 vector, whose first n entries are the system's current configuration (e.g., the joint angles) and whose remaining entries are the system's current configuration velocity (e.g., the joints' angular velocities) M_function A handle to a function that takes in a configuration vector and returns an nxn cell array, encoding the inertia matrix as a function of the configuration (e.g., the joint angles). dm_function: A handle to a function that takes in a configuration vector and returns a 1xn cell array, whose entries are the derivative of the inertia matrix with respect to configuration (e.g., the joint angles). F_function: A handle to a function that takes in a configuration vector, configuration velocity, and time, and returns an nx1 vector of configuration forces (e.g., the torques around the joints). % % Output: % % state velocity: A (2n)x1 vector, whose first n entries are the system's current configuration velocity (e.g., the joints' angular velocities), and whose remaining entries are the system's configuration acceleration (e.g., the joints' angular accelerations) Use the acceleration output of the Euler-Lagrange equations to construct a state-derivative function for a system with specified inertia, inertia-derivative, and force functions. In addition to standard Matlab functions, your code may assume that you have access to the following function(s) you created in previous assignments (along with the functions that they themselves call): ■ EulerLagrange_acceleration Remember that for these functions, the grading script will use the instructor's copy of the functions. function [state_velocity,.... configuration,... velocity,... acceleration] = Euler Lagrange_trajectory (time, state,M_function, dM_function, F_function) % Follow a trajectory whose acceleration is determined by an inertia matrix % and forcing function % % Inputs: % % % % % % % % % % % % % % % time: A scalar value describing the time at which the system dynamics are evaluated % 0/ state: A (2n)x1 vector, whose first n entries are the system's current configuration (e.g., the joint angles) and whose remaining entries are the system's current configuration velocity (e.g., the joints' angular velocities) M_function A handle to a function that takes in a configuration vector and returns an nxn cell array, encoding the inertia matrix as a function of the configuration (e.g., the joint angles). dm_function: A handle to a function that takes in a configuration vector and returns a 1xn cell array, whose entries are the derivative of the inertia matrix with respect to configuration (e.g., the joint angles). F_function: A handle to a function that takes in a configuration vector, configuration velocity, and time, and returns an nx1 vector of configuration forces (e.g., the torques around the joints). % % Output: % % state velocity: A (2n)x1 vector, whose first n entries are the system's current configuration velocity (e.g., the joints' angular velocities), and whose remaining entries are the system's configuration acceleration (e.g., the joints' angular accelerations)

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